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Modelling passive cardiac conductivity during ischaemia

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Abstract

The results of a geometric model of cardiac tissue, used to compute the bidomain conductivity tensors during three phases of ischaemia, are described. Ischaemic conditions were simulated by model parameters being changed to match the morphological and electrical changes of three phases of ischaemia reported in literature. The simulated changes included collapse of the interstitial space, cell swelling and the closure of gap junctions. The model contained 64 myocytes described by 2 million tetrahedral elements, to which an external electric field was applied, and then the finite element method was used to compute the associated current density. In the first case, a reduction in the amount of interstitial space led to a reduction in extracellular longitudinal conductivity by about 20%, which is in the range of reported literature values. Moderate cell swelling in the order of 10–20% did not affect extracellular conductivity considerably. To match the reported drop in total tissue conductance reported in experimental studies during the third phase of ischaemia, a ten fold increase in the gap junction resistance was simulated. This ten-fold increase correlates well with the reported changes in gap junction densities in the literature.

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References

  • Beardslee, M. A., Lerner, L. D., Tadros, P. N., Laing, J. G., Beyer, E. C., Yamada, K. A., Kléber, A. G., Schuessler, R. B., andSaffitz, J. E. (2000): ‘Dephosphyorylation and intracellular redistribution of ventricular connexin43 during electrical uncoupling induced by ischemia.Circ. Res.,87, pp. 656–662.

    Google Scholar 

  • Brown, A. M., Lee, K. S., andPowell, T. (1981): ‘Voltage clamp and internal perfusion of single rat heart muscle cells’,J. Physiol.,318, pp. 455–477

    Google Scholar 

  • Carmeliet, E. (1999): ‘Cardiac ionic currents and acute ischemia: from channels to arrhythmias,’Physiol. Rev.,79, pp. 917–1017.

    Google Scholar 

  • Chien, S., Usami, S., andSkalak, R. (1984): ‘Blood flow in small tubes’, inRenkin, E. M., andMichel, C. C. (Eds) ‘Handbook of physiology, section 2, The cardiovascular system, volume IV, Microcirculation part I’ (American Physiological Society, Bethesda, Maryland, 1984), pp. 217–249

    Google Scholar 

  • Cinca, J., Warren, M., Carreno, A., Tresanchez, M., Armadans, L., Gomez, P., Soler-Soler, J. (1997): ‘Changes in myocardial electrical impedance induced by coronary artery occlusion in pigs with and without preconditioning,’Circ.,96, pp. 3079–3086

    Google Scholar 

  • Duffy, H. S., Ashton, A. W., O'Donnell, P., Coombs, W., Taffet, S. M., Delmar, M., andSpray, D. C. (2004): ‘Regulation of Connexin43 protein complexes by intracellular acidification’,Circ. Res.,94, pp. 215–222

    Article  Google Scholar 

  • Fleischhauer, J., Lehmann, L., andKléber, A. G. (1995): ‘Electrical resistances of interstitial and microvascular space and determinants of the extracellular electrical field and velocity of propagation in ventricular myocardium,’Circ.,92, pp. 587–594

    Google Scholar 

  • Forbes, M. S., andSperelakis, N. (1995): ‘Ultrastructure of mammalian cardiac muscle,’Physiology and pathophysiology of the heart, 3rd edn‘ (Kluwer Academic Publishers, Norwell, MA, 1995). chap. 1, pp. 1–35

    Google Scholar 

  • Foster, K. R., andSchwan, H. P. (1989): ‘Dielectric properties of tissues and biological materials: a critical review’,Crit. Rev. Biomed. Eng.,17, pp. 25–104

    Google Scholar 

  • Henriquez, C. S., Tranqillo, J. V., Weinstein, D. M., Hsu, E. W., andJohnson, C. R. (2004): ‘Three-dimensional propagation in mathematic models: integrative model of the mouse heart’ (Saunders Company, Philadelphia, 2004), chap. 30, pp. 273–281

    Google Scholar 

  • Hopenfeld, B., Stinstra, J. G., andMacLeod, R. S. (2004): ‘A mechanism for ST depression associated with contiguous subendocardial ischemia’,J. Cardiovasc. Electrophysiol.,15, pp. 1200–1206

    Article  Google Scholar 

  • Hopenfeld, B., Stinstra, J. G., andMacLeod, R. S. (2005): ‘The effect of conductivity on ST-segment epicardial potentials arising from subendocardial ischemia’,Ann. Biomed. Eng.,33, pp. 751–763

    Article  Google Scholar 

  • Roth, B. J. (2004): ‘Two-dimensional propagation in cardiac muscle’ (Saunders Company, Philadelphia, 2004), chap. 29, pp. 267–272

    Google Scholar 

  • Jain, S. K., Schuessler, R. B., andSaffitz, J. E. (2003): ‘Mechanisms of delayed electrical uncoupling induced by ischemic preconditioning’,Circ. Res.,92, pp. 1138–1144

    Article  Google Scholar 

  • Kléber, A. G., andRiegger, C. B. (1987): ‘Electrical constants of arterially perfused rabbit papillary muscle’,J. Physiol.,385, pp. 307–324

    Google Scholar 

  • Metzger, P., andWeingart, R. (1985): ‘Electric current flow in cll pairs isolated from adult rat hearts’,J. Physiol.,366, pp. 177–195

    Google Scholar 

  • Owens, L. M., Fralix, T. A., Murphy, E., Cascio, W. E., andGettes, L. S. (1996): ‘Correlation of ischemia-induced extracellular and intracellular ion changes to cell-to-cell electrical uncoupling in isolated blood-perfused rabbit hearts’,Circ.,94, pp. 10–13

    Google Scholar 

  • Sachse, F. B. (2004): ‘Computational cardiology: modeling of anatomy, electrophysiology, and mechanic (LNCS 2966, Springer Press, Heidelberg, 2004)

    Google Scholar 

  • Schwann, H. P., andKay, C. F. (1956): ‘The conductivity of living tissues’,Ann. N.Y. Acad. Sci.,65, pp. 1007–1013

    Google Scholar 

  • Smith, W. T., Fleet, W. F., Johnson, T. A., Engle, C. L., andCascio, W. E. (1995): ‘The Ib phase of ventricular arrhythmias in ischemic in situ porcine heart is related to changes in cell-to-cell electrical coupling’,Circ.,92, pp. 3051–3060

    Google Scholar 

  • Steenbergen, C., Hill, M. L., andJennings, R. B. (1985): ‘Volume regulation and plasma membrane injury in aerobic, anaerobic, and ischemic myocardiumin vitro’,Circ. Res.,57, pp. 864–875

    Google Scholar 

  • Stinstra, J. G., Hopenfeld, B., andMacLeod, R. S. (2004): ‘Using models of the passive cardiac conductivity and full heart anisotropic bidomain to study the epicardial potentials in ischemia’. Proc., 26th Annual Int. Conf. of the IEEE Engineering in Medicine and Biology Soc., (2), pp. 3555–3558

    Google Scholar 

  • Stinstra, J. G., Hopenfeld, B., andMacLeod, R. S. (2005): ‘On the passive cardiac conductivity’,Ann. Biomed. Eng.,33, pp. 1743–1751

    Article  Google Scholar 

  • Stinstra, J. G., andPeters, M. J. (2002): ‘The influence of fetoabdominal tissues on fetal ECGs and MCGs’,Arch. Physiol. Biochem.,110, pp. 165–176

    Article  Google Scholar 

  • Tranum-Jensen, J., Janse, M. J., Fiolet, J. W. T., Krieger, W. J. G., D'Alnoncourt, C. N., andDurrer, D. (1981): ‘Tissue osmolality, cell swelling, and reperfusion in acute regional myocardial ischemia in the isolated porcine heart’,Circ. Res.,49, pp. 364–381

    Google Scholar 

  • Trautman, E. D., andNewbower, R. S. (1983): ‘A practical analysis of the electrical conductivity of blood’,IEEE Trans. Biomed. Eng.,30, pp. 141–153

    Google Scholar 

  • Weingart, R. (1986): ‘Electrical properties of the nexal membrane studied in rat ventricular cell pairs’,J. Physiol.,370, pp. 267–284

    Google Scholar 

  • Wright, A. R., andRees, S. A. (1998): ‘Cardiac cell volume: crystal clear or murky waters? A comparison with other cell types’,Pharmacol. Ther.,80, pp. 89–121

    Article  Google Scholar 

  • Yan, G. X., Chen, J., Yamada, K. A., Kléber, A. G., andCorr, P. B. (1996): ‘Contribution of shrinkage of extracellular space to extracellular K+ accumulation in myocardial ischemia of the rabbit’,J. Physiol.,490.1, pp. 215–228

    Google Scholar 

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Stinstra, J.G., Shome, S., Hopenfeld, B. et al. Modelling passive cardiac conductivity during ischaemia. Med. Biol. Eng. Comput. 43, 776–782 (2005). https://doi.org/10.1007/BF02430957

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  • DOI: https://doi.org/10.1007/BF02430957

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